Atkins & de Paula Atkins & de Paula: Elements of Physical Chemistry 6e Chapter 7: Chemical equilibria: the principles ©Oxford University Press, 2013. All rights reserved. Chemical Reaction - The Equation • Reaction equation for A reacting with B forming C and D A + B C + D (1) - general expression of a reaction v A + v B = v C + v D (2) - quantitative representation of a reaction A B → C D vAA + vBB vCC + vDD (3) - representing an equilibrium controlled reactio • Reaction stoichiometry ⇄ – vA, vB, vC and vD are numbers, called stoichiometry coefficients – The concept of mole (the number of molecules) in a chemical reaction – Determination of stoichiometry coefficients - balancing equation (equal number o each atom on both sides of the equation) e.g. 2NO + O2 = 2NO2 we have: 2 N, 4 O on both side Q. For the same reaction can we write the equation as 4 NO + 2 O2 = 4NO2 or NO + ½O2=NO2 ? Atkins & de Paula: Elements of Physical Chemistry 6e Direction of a Reaction Q. A reaction: A + B C + D. Will it proceed in the direction indicated? Is there a general way to know reaction direction? → A. We can tell from the change of Gibbs free energy in a reaction, G ∆ ° < reaction can proceed (we don’t know how fast it will be!) for a reaction at GT 0 Δ constant T, P, ∆GT ° = 0 reaction at equilibrium (no change in system - ‘dead’ state) we have ∆GT ° > 0 reaction will NOT proceed (or can proceed backward!) The 2nd Law of Thermodynamics - Processes occur in a direction of decreasing quality of energy. We need to study reaction system in terms of energies and their changes • The energies associated with a reaction system – Many energy terms, a, U, H, G, - all depend on 4 basic parameters: P, T, V, S – Usually P, T, V are specified by given reaction conditions. S is related to the substances in the reaction (reactants/products) and reaction conditions (P, T, V) – Knowing P, T, V and S, all other energy terms can be determined. The most important ones in relation to chemical reactions are H and G. Atkins & de Paula: Elements of Physical Chemistry 6e Entropy of Reaction System Entropy definition dS = dQ/T meaning: at T, change of S is proportional to change of heat. Entropy calculation Basis of S calculation: 3rd Law of thermodynamics: S = 0 at absolute T = 0. Assign standard entropy of a substance (1 mole, at 1 atm. 25°C) as = 298 0 298 (S°298 value of common substances are available� in most chemistry / chem. Eng. handbooks.) 0 The entropy change in a reaction at T, p This term becomes zero if there is no phase change during the reaction reaction:vAA + vBB D vCC + vDD = , = + + , , , , 0 0 0 0 0 푝 ∆ � − � Δ 298 � Δ If a reaction is adiabatic, it can only proceed when S>0 (reaction298 reaches equilibrium when S=0). Δ Usually S analysis of a reaction system is complicated and inconvenient to use. Δ Atkins & de Paula: Elements of Physical Chemistry 6e Enthalpy of Reaction System Enthalpy definition H = U+ pV ⇒ dH = dU + pdV + Vdp = S dT + Vdp ΔH = ΔU + Δn RT (gas, g-l, g-s, g-s,l phase at constant p and T) ΔH = ΔU (liquid, or solid (dV = 0)) Enthalpy calculation 0 Standard enthalpy of formation, Hf Assign H°f of all stable substances (O2, N2, CO2 H2O etc.) at 298K & 1atm as 0 (not at 0K as for S) (H°298 values of common substances are available in most chemistry / chem. eng. handbooks.) Enthalpy of combustion, Hc -Often used for combustion process, similar to enthalpy of formation Enthalpy change when 1 mole of substance combusted completely (reacted completely with O2). Atkins & de Paula: Elements of Physical Chemistry 6e Enthalpy of Reaction System The enthalpy change in a reaction at T, p reaction:vAA + vBB vCC + vDD =⇄ , , 0 0 0 ∆ � − �The ΔH of phase transformations including In which g-l-s or crystalline phase change = + + , , 0 0 298 푝푝 ΔH is a direct measureΔ of the reaction�298Δ heat associated� Δ with a reaction (if only chemical energy change exists). When ΔH < 0 - the reaction is exothermic and when ΔH > 0 is the reaction is endothermic. Reaction heat is of critical importance in reaction engineering (reactor and process design). Atkins & de Paula: Elements of Physical Chemistry 6e Gibbs Free Energy of Reaction System Gibbs Free Energy definition G = U + pV TS = H TS ⇒ ΔG = ΔH ΔS = ΔT + VΔp Gibbs free energy calculation − − − T − S 0 Standard Gibbs free energy, G298 Similar to S0 and H0, the standard Gibbs free energy of formation of a substance, G0, is defined at reference state of T=298 K and p = 1 atm (G°298 values of common substances are available in most chemistry / chem. eng. handbooks.) The enthalpy change in a reaction at T, p reaction:vAA + vBB vCC + vDD =⇄ , , 0 0 0 ∆ � − � In which , = , , (value of each individual substance) 0 0 0 0 = or, GT can Δbe determined Δ − directlyΔ from (value from overall reaction) 0 0 0 Δ Δ Δ − Δ Atkins & de Paula: Elements of Physical Chemistry 6e Gibbs Free Energy of Reaction System ΔG° is one of the most important thermodynamics properties for a chemical reaction system. - It determines the direction of reaction to proceed ∆ ° < reaction can proceed (we don’t know how fast it will be!) for a reaction at GT 0 constant T, p, ∆GT ° = 0 reaction at equilibrium (no further change in system) we have ∆GT ° > 0 reaction will NOT proceed (or can proceed backward!) • ΔG0 < 0 is the pre-condition which MUST be met for any process (not limited to chemical reaction systems) to occur (spontaneous process). • ΔG0 < 0 indicates a specified reaction has tendency to proceed; however, it CANNOT tell how fast that reaction will occur - reaction kinetics tell the reaction rate. • A process/reaction proceeds always in the direction of MINIMISING Gibbs free energy. This is a very important concept. • A process/reaction will stop at ΔG0 = 0, this is called equilibrium state. Atkins & de Paula: Elements of Physical Chemistry 6e Important Notes about S, H and G Δ Δ Δ S, H and G are widely used in analysing various systems. Our current discussion of these function is limited to the application to a reaction system. Δ Δ Δ A clear definition of the reaction conditions is necessary before start calculation of these properties. There are many ways these thermodynamic properties can be determined. Only most commonly used ones in relation to a chemical reaction are given. It is very important to understand the study a chemical reaction by means of thermodynamics tells only state - a ‘snapshot’ of system, and how a process proceeds from one state to another (reversible-irreversible, with or without work done / exchange heat with surrounding). There is no factor of time involved. Atkins & de Paula: Elements of Physical Chemistry 6e Gibbs energy minimum Extent of reaction ( ): The amount of reactants being converted to products. Its unit is mole. ξ In a very general way, the extent of reaction is calculated as d = dnA/vA (where v is the stoichiometric number of the reactant A, which is ξ A negative for the reactant!!) Why do we need a new quantity? Consider a generic reaction: 2A ↔ 3B The amount of A consumed is different from the amount of B produced. Which number should be used in the report? Consider: A ↔ B Assume an infinitesimal amount d of A turns into B, dn -d A ξ On the other hand, dn = d = ξ B Atkins & de Paula: Elements of Physical Chemistry 6e ξ Gibbs energy minimum Example 1: N2(g) + 3H2(g) ↔ 2NH3(g) When the extent of reaction changes from to mole, what are the changes of each reagent? ξ = 0 ξ = 1.0 Solution: identify vj: v(N2) = -1; v(H2) = -3; v(NH3) = 2. since d = 1.0 mole, dn(N ) = -1x1.0 mole = -1.0 mole, ξ 2 dn(H2) = -3x1.0 mole = -3.0 moles, dn(NH3) = 2x1.0 mole = 2.0 moles, Example 2: CH4(g) + Cl2(g) ↔ CHCl3(l) + HCl(g), in which the amount of reactant Cl2(g) decreases by 2 moles. What is the extent of the reaction? Solution: Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Atkins & de Paula: Elements of Physical Chemistry 6e Gibbs energy Variation of Gibbs energy during a reaction process Atkins & de Paula: Elements of Physical Chemistry 6e The reaction Gibbs energy: ΔrG The slope of the Gibbs energy plotted against the extent of reaction: = , ∆ here r signifies a derivative • A reaction for which rG is called exergonic. Δ • A reaction for which G is called endergonic. Δr < 0 • G , the forward reaction is spontaneous. r Δ > 0 • G , the reverse reaction is spontaneous. Δr < 0 G • Δ r > 0 , the reaction is at equilibrium!!! Δ = 0 Atkins & de Paula: Elements of Physical Chemistry 6e The reaction Gibbs energy Molecular interpretation of the minimum in the reaction Gibbs energy Gibbs energy of the system decreases as the reaction progress Gibbs energy of a system consisting of different portions of reactants and products Atkins & de Paula: Elements of Physical Chemistry 6e Calculation of reaction Gibbs energy Consider the reaction : A ↔ B initial amount: n n final amount: nAfA0 nBfB0 Ginitial Bn An G n n final = μB BfB0 + μA AfA0 G - G n n – n n ) =final μ initial+ μ B Bf A Af B A n - n n - n - ΔG = B Bf = (μA Af + μ ) B (μ B0 A+ μ A0 - ) = μ (B B0) + μ ( A0) = μ Δξ + μ ( Δξ) = (μ μA Δξ = = , ∆ − • When A B, the reaction (A → B) is spontaneous.